Question

An eccentric baseball card collector wants to distribute her collection among her descendants. If she divided her cards among her 17 great-great-grandchildren, there would be 3 cards left over. If she divided her cards among her 16 great-grandchildren, there would be 10 cards left over. If she divided her cards among her 11 grandchildren, there would be 4 cards left over. If she divided her cards among her 7 children, there would be no cards left over.

What is the smallest possible number of cards in her collection?

Answer 1

If we let x as the total number of baseball cards
and yn be the quotient per operation, then

x/17 = y1 + 3

x/16 = y2 + 10

x/11 = y3 + 4

x/7 = y4

Based on Equation 1, x must be greater than 17
Based on Equation 4, x must be divisible by 7
y1, y2, and y3 must all be whole numbers
The smallest possible number of cards is 70